There will be an auction of 90-day government bills next week. A discounted yield to maturity of 4.00 percent is widely expected to prevail at the auction. However, the bank for which you are working will regard the bills as a good investment only if it can obtain a discounted holding period yield of at least 4.25 percent.

The bank has some significant liabilities that are coming due 30 days after the auction. If the bank can get a discounted yield to maturity of at least 4.00 percent at auction, hold the bills for 30 days, and then sell them (in order to take care of the bank's liabilities), the bank's officers believe that they will have taken a risk that is worthwhile.

Given a par value of 100, what is the highest price that the bank would be willing to pay for the bill at auction?

If the discounted yield to maturity were, in fact, 4.00 percent at auction, what discounted yield to maturity would have to prevail after 30 days in order for the bank's discounted holding period yield to be 4.25 percent? What price would have to prevail for the bills at that time?